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A graph corresponding to the skeleton of one of the Archimedean solids. There are 13 Archimedean graphs, all of which are regular, planar, polyhedral, and Hamiltonian. The ...

The arithmetic-geometric matrix A_(AG) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt(d_i^2+d_j^2), (1) where d_i are the vertex degrees of the ...

Vince and Bóna (2012) define an assembly tree T for a connected simple graph G on n nodes as a binary rooted tree with n leavesTree Leaf and n-1 internal nodes and satisfying ...

The Balaban 10-cage is one of the three (3,10)-cage graphs (Read and Wilson 1998, p. 272). The Balaban (3,10)-cage was the first known example of a 10-cage (Balaban 1973, ...

An (n,k)-banana tree, as defined by Chen et al. (1997), is a graph obtained by connecting one leaf of each of n copies of an k-star graph with a single root vertex that is ...

The blossom algorithm (Edmonds 1965) finds a maximum independent edge set in a (possibly weighted) graph. While a maximum independent edge set can be found fairly easily for ...

Bouwer graphs, a term coined here for the first time, are a family of regular graphs which includes members that are symmetric but not arc-transitive. Such graphs are termed ...

Consider a broadcast scheme on a connected graph from an originator vertex v in a graph G consisting of a sequence of parallel calls starting from v. In each time step, every ...

The (connected) caveman graph is a graph arising in social network theory formed by modifying a set of isolated k-cliques (or "caves") by removing one edge from each clique ...

A Cayley tree is a tree in which each non-leaf graph vertex has a constant number of branches n is called an n-Cayley tree. 2-Cayley trees are path graphs. The unique ...